document.write( "Question 1138430: A motorboat travels 70mi in 2 hours going upstream. It travels 90mi going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? \n" ); document.write( "

Algebra.Com's Answer #756227 by ikleyn(52872) $\"\"$ $\"About$

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document.write( "Against the current the effective speed (the speed relative to the river bank) is\r\n" );
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document.write( "u - v =  = 35  miles per hour.     (1)   (u = the speed of the motorboat in still water;  v = the speed of the current)\r\n" );
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document.write( "With the current, the effective speed is\r\n" );
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document.write( "u + v =  =  45 miles per hour.     (2)\r\n" );
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document.write( "Add equations (1) and (2)\r\n" );
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document.write( "2u = 35 + 45 = 80  ====>  u = 80/2 = 40 mph is the speed of the motorboat in still water.    ANSWER\r\n" );
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document.write( "Subtract eq(1) from eq(2)\r\n" );
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document.write( "2v = 45 - 35 = 10  ====>  v = 10/2 = 5 mph  is the speed of the current.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution and the things to memorize are :\r
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document.write( "    1.  The effective speed of a boat traveling with    a current is the sum        of the two speeds.\r\n" );
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document.write( "    2.  The effective speed of a boat traveling against a current is the difference of the two speeds.\r\n" );
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document.write( "    3.  It gives a system of two equations in two unknowns, which fits very well to be solved by the elimination method.\r\n" );
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